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    <title>ss2tf</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>ss2tf</b> -  conversion from state-space to transfer function</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[h]=ss2tf(sl)   </tt>
      </dd>
      <dd>
        <tt>[Ds,NUM,chi]=ss2tf(sl)  </tt>
      </dd>
      <dd>
        <tt></tt>
      </dd>
      <dd>
        <tt>[h]=ss2tf(sl,"b")   </tt>
      </dd>
      <dd>
        <tt>[Ds,NUM,chi]=ss2tf(sl,"b")  </tt>
      </dd>
      <dd>
        <tt></tt>
      </dd>
      <dd>
        <tt></tt>
      </dd>
      <dd>
        <tt>[h]=ss2tf(sl,rmax)   </tt>
      </dd>
      <dd>
        <tt>[Ds,NUM,chi]=ss2tf(sl,rmax)  </tt>
      </dd>
      <dd>
        <tt></tt>
      </dd>
      <dd>
        <tt></tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>sl</b>
        </tt>: linear system (<tt>
          <b>syslin</b>
        </tt> list)</li>
      <li>
        <tt>
          <b>h</b>
        </tt>: transfer matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Called with three outputs <tt>
        <b>[Ds,NUM,chi]=ss2tf(sl)</b>
      </tt> returns 
    the numerator polynomial matrix <tt>
        <b>NUM</b>
      </tt>, the characteristic
    polynomial <tt>
        <b>chi</b>
      </tt> and the polynomial part <tt>
        <b>Ds</b>
      </tt> separately i.e.:</p>
    <pre>

h=NUM/chi + Ds
   
    </pre>
    <p>
    Method:</p>
    <p>
    One uses the characteristic polynomial and 
    <tt>
        <b>det(A+Eij)=det(A)+C(i,j)</b>
      </tt> where <tt>
        <b>C</b>
      </tt> is the adjugate 
    matrix of <tt>
        <b>A</b>
      </tt>.</p>
    <p>
    With <tt>
        <b>rmax</b>
      </tt> or <tt>
        <b>"b"</b>
      </tt> argument uses a block diagonalization of
    sl.A matrix and applies "Leverrier" algorithm on blocks.
    If given, <tt>
        <b>rmax</b>
      </tt> controls the conditionning (see bdiag).</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

s=poly(0,'s');
h=[1,1/s;1/(s^2+1),s/(s^2-2)]
sl=tf2ss(h);
h=clean(ss2tf(sl))
[Ds,NUM,chi]=ss2tf(sl)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="tf2ss.htm">
        <tt>
          <b>tf2ss</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../elementary/syslin.htm">
        <tt>
          <b>syslin</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/nlev.htm">
        <tt>
          <b>nlev</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/glever.htm">
        <tt>
          <b>glever</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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